A253834 -id:A253834

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A253935

T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically

+0
8

512, 2440, 2440, 8392, 8384, 8392, 28540, 30184, 30184, 28540, 91296, 109666, 124496, 109666, 91296, 263476, 299727, 451721, 451721, 299727, 263476, 709704, 756553, 992616, 1664470, 992616, 756553, 709704, 1850176, 1786831, 2326216

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OFFSET

1,1

COMMENTS

Table starts

......512.....2440.....8392....28540....91296...263476....709704...1850176

.....2440.....8384....30184...109666...299727...756553...1786831...3803056

.....8392....30184...124496...451721...992616..2326216...4928792...8796936

....28540...109666...451721..1664470..3152822..6795110..13179071..20815359

....91296...299727...992616..3152822..3515548..6348659...9470400..11628396

...263476...756553..2326216..6795110..6348659.11962178..17762028..22189517

...709704..1786831..4928792.13179071..9470400.17762028..31663440..40874791

..1850176..3803056..8796936.20815359.11628396.22189517..40874791..59454484

..4685448..7637333.15429736.34379873.17673400.34970988..67588814.103307903

.11503856.14786984.25901691.54238467.27050795.55170420.114752167.184797814

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1102

FORMULA

Empirical for column k:

k=1: [linear recurrence of order 32] for n>33

k=2: [order 46] for n>58

k=3: [order 53] for n>83

k=4: [order 54] for n>90

k=5: [order 46] for n>71

k=6: [order 47] for n>77

k=7: [order 54] for n>87

Empirical quasipolynomials for column k:

k=3: polynomial of degree 13 plus a quasipolynomial of degree 8 with period 24 for n>30

k=4: polynomial of degree 14 plus a quasipolynomial of degree 8 with period 24 for n>36

k=5: polynomial of degree 15 plus a quasipolynomial of degree 5 with period 24 for n>25

k=6: polynomial of degree 17 plus a quasipolynomial of degree 7 with period 24 for n>33

k=7: polynomial of degree 17 plus a quasipolynomial of degree 7 with period 24 for n>33

EXAMPLE

Some solutions for n=3 k=4

..0..1..0..0..1..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..1..0..0

..1..1..0..1..1..1....0..0..0..1..1..0....1..0..0..1..1..1....1..0..0..1..0..1

..0..0..0..1..0..1....0..1..0..1..1..1....0..0..0..1..1..0....0..0..0..1..0..1

..0..1..1..1..0..1....1..1..0..1..0..0....0..1..0..1..1..0....0..0..0..1..1..1

..0..0..1..1..1..1....0..0..1..1..0..1....0..1..1..1..0..1....1..0..1..1..0..1

CROSSREFS

Column 1 is A253834

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 19 2015

STATUS

approved

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